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Mirrors > Home > ILE Home > Th. List > albidv | GIF version |
Description: Formula-building rule for universal quantifier (deduction form). (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
albidv.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
albidv | ⊢ (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1526 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | albidv.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
3 | 1, 2 | albidh 1480 | 1 ⊢ (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 105 ∀wal 1351 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-17 1526 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: ax11v 1827 2albidv 1867 sbal1yz 2001 eujust 2028 euf 2031 mo23 2067 axext3 2160 bm1.1 2162 eqeq1 2184 cbvabw 2300 nfceqdf 2318 ralbidv2 2479 alexeq 2864 pm13.183 2876 eqeu 2908 mo2icl 2917 euind 2925 reuind 2943 cdeqal 2952 sbcal 3015 sbcalg 3016 sbcabel 3045 csbcow 3069 csbiebg 3100 ssconb 3269 reldisj 3475 sbcssg 3533 elint 3851 axsep2 4123 zfauscl 4124 bm1.3ii 4125 exmidel 4206 euotd 4255 freq1 4345 freq2 4347 eusv1 4453 ontr2exmid 4525 regexmid 4535 tfisi 4587 nnregexmid 4621 iota5 5199 sbcfung 5241 funimass4 5567 dffo3 5664 eufnfv 5748 dff13 5769 tfr1onlemsucfn 6341 tfr1onlemsucaccv 6342 tfr1onlembxssdm 6344 tfr1onlembfn 6345 tfrcllemsucfn 6354 tfrcllemsucaccv 6355 tfrcllembxssdm 6357 tfrcllembfn 6358 tfrcl 6365 frecabcl 6400 ssfiexmid 6876 domfiexmid 6878 diffitest 6887 findcard 6888 findcard2 6889 findcard2s 6890 fiintim 6928 fisseneq 6931 isomni 7134 isomnimap 7135 ismkv 7151 ismkvmap 7152 iswomni 7163 iswomnimap 7164 omniwomnimkv 7165 exmidfodomrlemr 7201 exmidfodomrlemrALT 7202 fz1sbc 10096 frecuzrdgtcl 10412 frecuzrdgfunlem 10419 zfz1iso 10821 istopg 13502 bdsep2 14641 bdsepnfALT 14644 bdzfauscl 14645 bdbm1.3ii 14646 bj-2inf 14693 bj-nn0sucALT 14733 sscoll2 14743 |
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